Mathematics II - Old Questions

16. Let   be a linear transformation. Then T is one-to-one if and only if the equation T(x) = 0

has only the trivial solution, prove the statement.

OR

Let  and define Then

a) Find T(u)

b) Find an whose image under T is b.

c) Is there more than one x whose image under T is b?

d) Determine if c is the range of T.